Question: Rewrite as a simplified fraction. ${0.8\overline{92} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 892.9292...\\ 10x &= 8.9292...\end{align*}}$ Subtracting the two equations, we have: ${990x = 884}$ ${x = \dfrac{884}{990}} $ ${x = \dfrac{442}{495}} $